Amir, Rabah (Iowa University): «On the microeconomic foundations of linear demand for differentiated products» (joint with Philip Erickson and Jim Jin). This paper provides a thorough exploration of the microeconomic foundations for the multi-variate linear demand function for differentiated products that is widely used in industrial organization. A key finding is that strict concavity of the quadratic utility function is critical for the demand system to be well defined. Otherwise, the true demand function may be quite complex: Multi-valued, non-linear and income-dependent. The solution of the first order conditions for the consumer problem, which we call a local demand function, may have quite pathological properties. We uncover failures of duality relationships between substitute products and complementary products, as well as the incompatibility between high levels of complementarity and concavity. The two-good case emerges as a special case with strong, but surprisingly non-robust properties. A key implication is that all conclusions derived via the use of linear demand that does not satisfy the Law of Demand ought to be regarded with some suspicion.
Bich, Philippe (Paris School of Economics and University of Paris 1): «On Temporal Aggregators and Dynamic Programming» (joint with Jean-Pierre Drugeon and Lisa Morhaim).
In the tradition of Irving Fisher, the current article advocates an approach to dynamic programming that is based upon elementary aggregating functions where current action and future expected payoff combine to yield overall current payoff. Some regularity properties are provided on the aggregator which allow for establishing the existence, the uniqueness and the computation of the Bellman equation. Some order-theoretic foundations for such aggregators are also established. The aggregator line of argument encompasses and generalizes many previous results based upon additive or non-additive recursive payoff functions.
Araujo, Aloisio (Getulio Vargas Foundation, IMPA): «Refinement of Dynamic Equilibrium» (joint with M. Choubdar, W.L. Maldonado, D. Pinheiro and A.A. Pinto).
In this paper we propose a refinement of dynamic equilibria based on small random deviations from the perfect foresight equilibrium in a class of one step forward dynamic models. Specifically, when the backward per- fect foresight (bpf) map is a unimodal function exhibiting cycles or complex dynamics, we define a small random deviation from the perfect foresight equi- librium as a sequence of random variables generated from small stochastic errors on the perfect prevision of the future state variable value. First, we show that the stochastic process generated in that way is stationary provided that the support of the perturbation is small enough. Second, when the bpf map exhibits ergodic chaos, we show that the stationary measures converge to the Bowen-Ruelle-Sinai invariant measure of the bpf map as the size of the perturbations approaches zero. Third, if the bpf map has an attracting cycle, then the stationary measure is close to a convex linear combination of Dirac measures supported on that cycle. Therefore, depending on the parameter value which defines the bpf map, small random deviations are close to combi- nation of Dirac measures supported on a determinate cycle or to the stationary measure of the chaotic sunspot equilibrium defined by Araujo and Maldonado (2000). Neither indeterminate cycles nor other kind of sunspot equilibrium is found as the limiting behavior of the small random deviations. Finally, we provide two examples - the classical overlapping generations model with fiat money and the Shapley-Shubik market game - to illustrate the refinement of the dynamic equilibria in those models given by the small random deviations from the perfect foresight equilibrium.
Dziewulski, Pawel (Oxford University): «Revealed Time Preference». In this paper we present the observable implications of the discounted utility model of time-preference. We consider a framework in which subjects are allowed to choose between pairs consisting of a reward and a time-delay at which the prize is delivered. Given a finite set of observations, we discuss conditions under which the choices can be rationalised by a discounted utility maximisation. We develop an axiomatic characterisation of time-preference with various forms of discounting, including weakly present-biased, quasi-hyperbolic, and exponential, and determine the testable restrictions for each specification. Moreover, we discuss possible identification issues that may arise in this class of tests. Finally, we apply our methods to study the impact of substance abuse on time-preference.
Cornet, Bernard (University of Paris 1 and Kansas University): «Ambiguity models in intertemporal financial markets». This paper characterizes arbitrage-free financial markets with bid/ask spreads that are submodular, i.e., their super-replication cost functions (or super-hedging prices) are submodular, and studies an important class of submodular markets. The sub- modular assumption on the cost function, or the supermodularity usually assumed on preferences and utility functions, is the formal expression of perfect complemen- tarity, which dates back to Fisher, Pareto, and Edgeworth, according to Samuelson. Arbitrage-free markets whose bond is frictionless provide a natural rationale for the famous multi-prior model of Gilboa and Schmeidler, extensively used in this paper in its dual form. Actually, the absence of arbitrage opportunities in the market exhibits a family of risk-neutral probability measures, leading to a super-replication cost `a la Gilboa-Schmeidler. Our characterization result is two-fold. First, a market is submodular if and only if its super-replication cost is a Choquet integral and if and only if its set of risk- neutral probabilities is representable as the core of a submodular non-additive prob- ability that is uniquely defined, called risk-neutral capacity. Second, a market is representable by its risk neutral capacity if and only if it is equivalent to a market, only composed of bid/ask event securities, i.e., whose payoffs are characteristic func- tions of events. Our second contribution is to study an important class of financial markets, only composed of bid/ask event securities. Our main result shows that such a market is submodular if the bond is frictionless and the events (other than the sure event) defining the securities are pairwise disjoint, hence in particular, if they are are bid/ask Arrow securities. The super-replication cost can then be calculated as a Choquet integral with respect to the risk-neutral capacity, which is moreover given by an explicit and tractable formula.
Faro, Jose Heleno (Insper, Brazil): «Bewley 'meet' Gilboa and Schmeidler: Legitimate Preferences under Uncertainty» (joint with Efe Ok and Gil Riella). We model an organization or a corporation by a preference relation over uncertain acts satisfying a set of axioms capturing a legitimate decision making process. We show that our set of behavioral conditions is equivalent to a representation of legitimate preferences: there exist two nested sets of priors in which the smaller one represents the set of priors from individuals who occupy higher positions within the organization, while the larger one takes into account also probabilistic beliefs from people of lower positions. A legitimate decision that supports an act f against an act g includes authorization, which occurs when the smaller set of priors unanimously deems the act f better than the act g, a la Bewley (2002), and endorsement, which occurs when the larger set of priors deems the act f better than the act g according to a maxmin rule a la Gilboa and Schmeidler (1989). We also provide some results concerning the comparative statics feature by legitimate preferences in both aspects of authorization and endorsement rules.
Jensen, Martin Kaae (University of Leicester): «Robust Predictions in the Large». Tools such as the implicit function theorem (IFT) and robust comparative statics (RCS) apply when changes in exogenous parameters are small (infinitesimal). While RCS also applies to changes that are large (non-infinitesimal), any prediction that is true for a large parameter change but not for a small one will go undetected. Think of an increase in a tax rate from 47 to 50 %, and ask if aggregate income goes up or down in some macroeconomic model. Robust methods as well as standard applications of the IFT may come up inconclusive because they depend on the endogenous response also manifesting itself for an increase of 2, 1, 0.1, 0.01 (etc) percentage points. In particular, these methods only ever provide necessary conditions in so far as the conditions must be necessary for a small change also. The aim of this paper, is to present comparative statics tools that apply in the large without imposing the necessity of also holding in the small. The methods apply to systems of equilibrium equations and so present a (multi-dimensional) parallel to the results in Milgrom and Roberts (AER, 1994). Simple and easily verifiable conditions on individual agents are given that imply results in the large in situations where both the IFT and RCS are inconclusive. In the talk, contests and Cournot duopoly are considered as examples (neither is a game of strategic complementarities, and in either case the IFT is inconclusive at the individual level when symmetry is not imposed). The main mathematical ingredients are the Poincare-Hopf theorem and various “Milnor type” approximations.
Kamihigashi, Takashi (University of Kobe): «Robust Comparative Statics of Non-Monotone Shocks in Large Aggregative Games» (joint with Carmen Camacho and Cagri Saglam). A policy change that involves redistribution of income or wealth is typically controversial, affecting some people positively but others negatively. In this paper we extend the "robust comparative statics" result on large aggregative games established by Acemoglu and Jensen (2010, 49th IEEE Conference on Decision and Control, 3133-3139) to possibly controversial policy changes. In particular, we show that both the smallest and the largest equilibrium values of an aggregate variable increase in response to a policy change to which individuals' reactions may be mixed but the overall aggregate response is positive. We provide sufficient conditions for such a policy change in terms of distributional changes in parameters.
Ok, Efe (New York University): «Conditional Expected Multi-Utility Theory» (joint with Kazuhiro Hara and Gil Riella).This paper begins by observing that any reáexive binary (preference) relation (over risky prospects which satisies the Independence Axiom admits a form of expected utility representation. We refer to this representation notion a coalitional minmax expected utility representation. By adding the remaining properties of the expected utility theorem, namely, continuity, completeness and transitivity, one by one, we find how this representation gets sharper and sharper, thereby deducing the versions of this classical theorem in which any combination of these properties are dropped from its statement. This approach also allows us to weaken transitivity in this theorem, rather than eliminating it entirely, say, to quasitransitivity or acyclicity. Apart from providing a unified dissection of the expected utility theorem, these results are relevant for the growing literature on boundedly rational choice in which revealed preference relations often lack the properties of completeness and/or transitivity (but often satisfy the Independence Axiom). Finally,and perhaps more importantly, we show that our representation theorems allow us to answer many economic questions that are posed in terms of nontransitive/incomplete preferences, say, about the maximization of preferences, existence of Nash equilibrium, preference for portfolio diversification, and possibility of the preference reversal phenomenon.
Pivato, Marcus (University of Cergy): «Subjective expected utility representations for Savage preferences on topological spaces.» (joint with Vassili Vergopoulos). In many situations of decision-making under uncertainty, the set of possible states of the world and the set of possible outcomes each have a topological structure, and the only feasible acts are those where the outcome varies continuously with the state. Indeed, in some situations, the only feasible acts are differentiable functions. Savage's (1954) axioms do not apply to such a restricted domain of acts. Nevertheless, we axiomatically characterize a Subjective Expected Utility (SEU) representation of ex ante preferences in this environment. Our SEU representation involves a unique Borel probability measure on the state space, and an essentially unique, continuous utility function on the outcome space.
Polisson, Matthew (University of Leicester): «Revealed Preferences over Risk and Uncertainty.» (joint with John Quah and Ludovic Renou) We develop a nonparametric procedure for testing the consistency of contingent consumption data with a broad class of models of choice under risk and under uncertainty. Our procedure allows for risk loving and elation seeking behavior and can be used to calculate the magnitude of violations from a particular model of choice, with an index first suggested by Afriat (1972, 1973). With this index, we evaluate different models (including expected utility and disappointment aversion) in the data collected by Choi et al. (2007). Among those subjects exhibiting choice behavior consistent with the maximization of some increasing utility function, more than half are consistent with models of expected utility and disappointment aversion.
Sabarwal, Tarun (University of Kansas): «Directional Monotone Comparative Statics». Many questions of interest in economics can be stated in terms of monotone comparative statics: If a parameter of a constrained optimization problem "increases," when does its solution "increase'" as well. This paper characterizes monotone comparative statics in different directions in finite-dimensional Euclidean space. The characterizations are ordinal and retain the same flavor as their counterparts in the standard theory, showing new connections to the standard theory. The results are highlighted by applications in different areas such as consumer theory, producer theory, and game theory, including applications to consumer demand, theory of competition, labor-leisure decisions with discrete choices, environmental emissions standards, and auctions. These indicate new applications and also enhance the reach of existing results. The formulation here allows flexibility to explore comparative statics with respect to the constraint set, with respect to parameters in the objective function, or both. It does not require new binary relations or convex domains. Results from Quah (2007) are included as a special case.
Sato, Kenji (Kobe University): «Differentiable Monotone Comparative Statics» (joint with Takashi Kamihigashi). Continuity and differentiability of optimal decision are the basis for various economic analyses and predictions. The present paper demonstrates these properties hold almost everywhere for problems having strongly monotone optimal correspondence. Results in the literature of monotone comparative statics are readily applicable to show that some economic models, such as a supermodular game and capital accumulation model, have almost everywhere differentiable policy.
Stinchcombe, Maxwell (The University of Texas at Austin): «Stochastic Choice and Optimal Sequential Sampling» (joint with Urmee Kahn). Society is an aggregate of present and future generations. We study stochastic societal optimization problems in which similar treatment of generations in similar situations is possible. For such problems, all patient, inequality averse societal welfare functions that are perfectly Pareto responsive have the same optimal policies. When the outcomes of irreversible decisions are partially learnable, the optimal policies for patience preferences yield a variant of the precautionary principle. Under mild conditions, optimal policies exist and there is a single Bellman-like equation characterizing them.
Strzalecki, Tomasz (Harvard University): «Stochastic Choice and Optimal Sequential Sampling» (joint with Drew Fudenberg and Philipp Strack). We model the joint distribution of choice probabilities and decision times in bi- nary decisions as the solution to a problem of optimal sequential sampling, where the agent is uncertain of the utility of each action and pays a constant cost per unit time for gathering information. We show that choices are more likely to be correct when the agent chooses to decide quickly provided that the agent’s prior beliefs are correct. This better matches the observed correlation between decision time and choice probability than does the classical drift-diffusion model, where the agent knows the utility difference between the choices.
Suen, Richard (University of Leicester): «Concave Consumption Function and Precautionary Wealth Accumulation». This paper examines the theoretical foundations of precautionary saving behaviour in a canonical life-cycle model where consumers face uninsurable idiosyncratic labour income risk and borrowing constraints. We begin by characterizing the consumption function of individual consumers. We show that the consumption function is concave when the utility function has strictly positive third derivative and the inverse of absolute prudence is a concave function. These conditions encompass all HARA utility functions with strictly positive third derivative as special cases. We then show that when consumption function is concave, a mean-preserving increase in income risks would encourage wealth accumulation at both the individual and aggregate levels.
Wakker, Peter (Erasmus University): «The Present State of the Art in Risk- and Ambiguity Decision Theory as an Interaction between Mathematical Economists and Psychologists»
The new behavioral approach in economics pervades in intertemporal choice, game theory, and more and more in every economic discipline. Its start, and most advanced development up to today, is in decision under risk and uncertainty, or ambiguity as is the fashionable term today. Here it started with the introduction of nonexpected utility models in the first FUR conferences, from which it spread more and more, to become what is called the behavioral approach nowadays. It involves more sophisticated theories than in the classical approach. This lecture describes how the current state of the art in the behavioral approach could only come about from interactions between empirically oriented psychologists and mathematically oriented economists. At several stages in history, the next step forward could be made only by empirical intuitions from psychologists. Following up on that, the next step forward could be made only by theoretical inputs from economists with advanced technical skills. Modern views on the proper modeling of utility, beliefs, risk, and ambiguity attitudes could only arise from the merger of ideas from all the fields mentioned. The lecture ends with speculations on future directions of risk and ambiguity theories and their implications for other economic disciplines.
Yildiz, Muhamet (Massachussets Institute of Technology): «Crises: Equilibrium Shifts under Model Uncertainty» (joint with Stephen Morris). The talk will be based on our work on global games analysis with fat tailed distributions that often arise with model uncertainty. We consider a dynamic investment game in which a continuum of players repeatedly invest in projects. In each period, each player’s payoff from investment is the sum of a fundamental that follows a random walk, the measure of the players who invest in that period, and an idiosyncratic shock. We assume that the shocks to the fundamental (i.e., the steps in the random walk) have thicker tails than the idiosyncratic shocks, reflecting a situation in which players face a large uncertainty about the model that affects all players simultaneously. In normal times, i.e., when players’ payoffs are close to the previous value of the fundamental, they update their payoffs as in the usual thin tailed models and attribute some of the deviation in their payoffs from the previous value of the fundamental to a shock in the fundamental and some of it to their own idiosyncratic payoff shocks. For such types, both investment and not investment can be supported as an equilibrium action, and we select the equilibrium in which the equilibrium actions do not change spuriously. On the other hand, at times of crises, i.e., when the players’ payoffs are far from the previous value of the fundamental, the players attribute all the deviation to a shock to the fundamental, concluding that all players received such large payoff shocks. This leads to risk-dominance as the unique solution for those types. Now, without a crisis, due to inertia, investment cycle lags the fundamental cycle. In recovery and booms, when the fundamental is rising, the players start investing much later than the time investment becomes risk dominant, and in busts, when the fundamental is deteriorating, they stop investing much later than investment becomes risk-dominated. The crises lead to equilibrium shifts by switching to the risk dominant action. A negative shock in good times with deteriorating fundamental leads to immediate non-investment which would have come much later without a shock. Similarly, a positive shock in an early part of recovery helps accelerating the investment.